Universität Wien
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250025 VO Introduction to topology (2019W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Das 3. Kolloquium am 30.04 wird auf den 07.05.2020 verschoben und findet als digitale offline Prüfung statt, d.h. die Angaben können über moodle heruntergeladen werden und werden zum Prüfungsende auf moodle hochgeladen. Nähere Informationen zum 4. Kolloquium werden noch bekannt gegeben.

  • Thursday 03.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.12. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.01. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Notions like neighbourhood, convergence, continuity, connectedness already play an important role in the courses on analysis. Set theoretic topology
examines the properties of these notions in great generality. To this end it axiomatizes the concept of neighbourhood (or equivalently that of an open set) in the central notion of topological space. Only building on this it is possible
to define concepts like convergence, continuity, connectedness and compactness and to examine their properties. Due to this great generality of its notions topology
has applications to a wide area of mathematics and in particular then makes possible to argue using geometric intuition (based on the notion of neighbourhood). Topology thus has become a foundational theory of mathematics.

Content of the course: Departing from the courses Analysis 1 and 2 where topological notions appear for the first time we will introduce general topological spaces and study the basic topological
concepts convergence, continuity, compactness, connectedness and also techniques for constructing topological spaces.

Aims: Knowledge and understanding of basic notions and methods of topology and their properties.
Understanding of applicability of abstract notions of topology e.g. in analysis.

Assessment and permitted materials

Written exam. No aids are permitted.

Minimum requirements and assessment criteria

50 percent of the maximum score of the written exam

Examination topics

Content of the course

Reading list

v. Querenburg: Mengentheoretische Topologie

Jänich: Topologie

Dixmier: General Topology

Laures, Szymik: Grundkurs Topologie

Bartsch: Allgemeine Topologie

Bourbaki: Topology

Schubert: Topologie

Association in the course directory

TFA

Last modified: Fr 12.05.2023 00:21